function cov_plot = plot_cov_over_nu(empirical_cov_list, meta_nu_list, EB_nu)
    
    cov_plot = figure;
    hold on;
    
    % Plot each line with a unique color and set display names for the legend
    plot(meta_nu_list, empirical_cov_list, 'k', 'LineWidth', 1.2);
    
    % Find the y-value at EB_nu using interpolation
    y_value = interp1(meta_nu_list, empirical_cov_list, EB_nu);
    plot(EB_nu, y_value, 'x', 'Color', 'k', 'MarkerSize', 12, 'LineWidth', 1.5, 'HandleVisibility', 'off');

    % Add a dashed reference line at y = 0.8
    yline(0.8, 'k--', 'LineWidth', 1, 'HandleVisibility', 'off');
    ylim([0.7, 0.9])
    
    set(gca, 'FontSize', 16);
    set(gca, 'TickLabelInterpreter', 'latex');
    
    hold off;

end